QUESTION $4$:

A piston is propagating sound waves from a baffled region by moving the air in front of it$.$ The sound power is measured to be $100$ Watts. The radius of the piston is $0\mathrm{.}5$ m $.$ The piston is excited at a high frequency $($i$.$e$.$ ka$>>1).$ The mass of the piston is $50$ grams and the stiffness of the rod which is used to push the piston is $\backslash (3\backslash$times $10^\{6\}\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )($mass of the rod and the viscous damping of the system is small enough to ignore$).$

a$.$ It is observed that the velocity of the piston and the force applied to push the piston system are in phase. Find the frequency of the applied force. $(\backslash (7560\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ))$

b$.$ Find the amplitude of the forcing applied. $(255\mathrm{.}3$ N$)$